Details

sample39.0ms

Algorithm

intervals

Results

25.0ms

590×

body

valid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	26	8
1	51	8
2	88	7
3	153	7
4	357	7
5	1572	7
6	5002	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (* b b))
0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
0.0b	(+ (* a a) (* b b))
0.4b	(pow (+ (* a a) (* b b)) 2.0)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-exp-log` `add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
8×	`fma-def` `add-log-exp`
6×	`unpow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`+-commutative` `flip3-+` `sum-log` `flip-+` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `associate-r` `pow-exp` `*-commutative` `unswap-sqr`

Counts

4 → 74

Calls

4 calls:

7.0ms	(* 4.0 (* b b))
28.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
3.0ms	(+ (* a a) (* b b))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)

series220.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 4.0 (* b b))
65.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
26.0ms	(+ (* a a) (* b b))
104.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify42.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	339	438
1	1458	396
2	5002	385

prune210.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (fma (pow b 2) (+ 4.0 (* 2 (pow a 2))) (pow a 4)) 1.0)
0.0b	(* 2 (pow a 2))
0.0b	(fma (pow b 2) (+ 4.0 (* 2 (pow a 2))) (pow a 4))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
9×	`prod-diff`
8×	`add-exp-log` `associate-r`
5×	`add-cbrt-cube` `add-log-exp`
4×	`unpow-prod-down` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `fma-neg` `associate-l` `prod-exp` `log1p-expm1-u`
2×	`fma-udef` `unpow2` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `pow-exp` `associate--l+` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 68

Calls

3 calls:

3.0ms	(- (fma (pow b 2) (+ 4.0 (* 2 (pow a 2))) (pow a 4)) 1.0)
6.0ms	(* 2 (pow a 2))
0.0ms	(fma (pow b 2) (+ 4.0 (* 2 (pow a 2))) (pow a 4))

series168.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(- (fma (pow b 2) (+ 4.0 (* 2 (pow a 2))) (pow a 4)) 1.0)
24.0ms	(* 2 (pow a 2))
69.0ms	(fma (pow b 2) (+ 4.0 (* 2 (pow a 2))) (pow a 4))

simplify41.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	259	614
1	1045	483
2	5001	476

prune195.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2.0 (pow a 2))
0.0b	(* 4.0 (* b b))
0.0b	(+ (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) (* 4.0 (* b b)))
0.8b	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`pow1` `add-cube-cbrt` `-un-lft-identity` `associate-r*`
6×	`associate-l` `prod-exp` `add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `unpow-prod-down` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-def` `pow-prod-down`
2×	`*-commutative` `fma-udef` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+l+` `flip3-+` `pow-exp` `sum-log` `flip-+`

Counts

4 → 77

Calls

4 calls:

6.0ms	(* 2.0 (pow a 2))
7.0ms	(* 4.0 (* b b))
3.0ms	(+ (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) (* 4.0 (* b b)))
0.0ms	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

series185.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 2.0 (pow a 2))
24.0ms	(* 4.0 (* b b))
64.0ms	(+ (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) (* 4.0 (* b b)))
73.0ms	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

simplify41.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	291	467
1	1199	418
2	5001	407

prune245.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes47.0ms

Accuracy

88.6% (1.3b remaining)

Error of 1.5b against oracle of 0.1b and baseline of 11.7b

bsearch88.0ms

Steps

Iters	Range		Point
7	2.8172906988900064e-06	6.0755399135969525e-05	6.021731686857214e-05
8	-0.12347723982223391	-6.246474786567043e-06	-0.00024246602164438788

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	16
1	35	16

end0.0ms

sample1.2s

Algorithm

intervals

Results

814.0ms

20363×

body

valid